Essential linear algebra with applications a problem-solving approach /
This textbook provides a rigorous introduction to linear algebra in addition to material suitable for a more advanced course while emphasizing the subject?s interactions with other topics in mathematics such as calculus and geometry. A problem-based approach is used to develop the theoretical founda...
| Main Author: | Andreescu, Titu, 1956- |
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| Other Authors: | SpringerLink (Online service) |
| Format: | eBook |
| Language: | English |
| Published: |
New York, NY :
Birkhäuser,
2014.
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| Physical Description: |
1 online resource (x, 491 pages) : color illustrations. |
| Subjects: |
| Summary: |
This textbook provides a rigorous introduction to linear algebra in addition to material suitable for a more advanced course while emphasizing the subject?s interactions with other topics in mathematics such as calculus and geometry. A problem-based approach is used to develop the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality. Key features include:? a thorough presentation of the main results in linear algebra along with numerous examples to illustrate the theory;? over 500 problems (half with complete solutions) carefully selected for their elegance and theoretical significance;? an interleaved discussion of geometry and linear algebra, giving readers a solid understanding of both topics and the relationship between them. Numerous exercises and well-chosen examples make this text suitable for advanced courses at the junior or senior levels. It can also serve as a source of supplementary problems for a sophomore-level course. |
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| Item Description: |
Preface -- Linear Phenomena and Euclidean Spaces of Small Dimension -- Concrete Vector Spaces -- Vector Spaces and Subspaces -- Linear Transformations -- More Matrix Algebra and Determinants -- General Theory of Linear Equations -- Eigenvectors -- Orthogonality -- Forms -- Vector Spaces over Finite Fields -- Appendix A: Complex Numbers -- Appendix B: Polynomials over Complex Numbers -- References -- Index. This textbook provides a rigorous introduction to linear algebra in addition to material suitable for a more advanced course while emphasizing the subject?s interactions with other topics in mathematics such as calculus and geometry. A problem-based approach is used to develop the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality. Key features include:? a thorough presentation of the main results in linear algebra along with numerous examples to illustrate the theory;? over 500 problems (half with complete solutions) carefully selected for their elegance and theoretical significance;? an interleaved discussion of geometry and linear algebra, giving readers a solid understanding of both topics and the relationship between them. Numerous exercises and well-chosen examples make this text suitable for advanced courses at the junior or senior levels. It can also serve as a source of supplementary problems for a sophomore-level course. Includes bibliographical references. English. |
| Physical Description: |
1 online resource (x, 491 pages) : color illustrations. |
| Bibliography: |
Includes bibliographical references. |
| ISBN: |
9780817646363 0817646361 0817643605 9780817643607 |